Perspective Unlimited

Thursday, August 30, 2007

Insurance Misunderstood

In 2005, Liverpool reached the finals of the Champions League (European Cup) for the first time in 21 years. Liverpool was clearly underdog to the stylish AC Milan. Big underdog. A lot was riding on that one match - Liverpool was 5th in the league that year, which meant they would not qualify for the competition the next season if they didn't win. Their captain, Steven Gerrard, would probably have gone to Chelski if that happened. These were terrible prospects for a Liverpool supporter like myself.

Should I Bet on My Team?

The question was: Should a Liverpool supporter bet on Liverpool or AC Milan? (do answer or make a guess before you read on).

Suppose I was risk-averse and that I placed a bet with AC Milan. If AC Milan won, I would be compensated monetarily instead by winning the bet. If Liverpool won, the amount I placed on the bet would be lost, but it would hardly matter since the joy of seeing my team win would be great. Effectively, placing a bet against my favourite team Liverpool (and on AC Milan) became an insurance policy for me. On the other hand, placing a bet on Liverpool would have exposed me to more risk since I could potentially suffer the double agony of losing both game and bet.

What appears counter-intuitive to the lay person becomes perfectly rational for a trained economist - betting against your favourite team is the route to greater happiness! It sometimes comes as a surprise to me how few people understand this principle. Even when I pose this question to a class of economics undergraduates, 80 per cent would get it wrong despite hours of lectures and classes on insurance.

History would show that I didn't win my bet on AC Milan in 2005, but did it imply that I "lost"?

The Outcome You Do Not Want

The simple example provides an important lesson - always bet on the outcome you do not want for insurance. You buy a car insurance so that you can receive compensation when you get into an accident. If you "win" the bet with the car insurance company, you would have been involved in an accident already - clearly an outcome you do not want! When you "win", you have in fact already lost.

Therefore, my bet on AC Milan was actually one I would rather not win. Likewise, I would rather pay for healthcare insurance and never have to claim it. When it comes to insurance, it is not a good thing in general to "win" against the house (insurance provider)! The notion that we should buy insurance and try to win against the house is simply preposterous.

Purchasing an insurance guards the individual against downsides. For the risk-averse individual, the insurance offers a peace of mind which improves his welfare regardless whether the payout is claimed or not. A car insurance gives me the peace of mind to drive on the roads - knowing that my financial losses are covered. I buy because I am risk-averse. Whether I get a payout or not in the end - surprise surprise - is actually a moot point.

All Can Be Better Off

Let me turn to the longevity insurance proposed by the government (my writeup here). Many bloggers believe that if an individual does not live till 85 to get the payout, he would have "lost" the bet against the house and be worse off as a result of having paid the premium all those years. I hope by now the reader can see that this is an unsound understanding of insurance. Insurance is not a zero-sum game, one does not lose just because he is not getting the payout.

The idea of an insurance policy is that with a small payment, an individual can guard himself against desperate outcomes, thereby offering a peace of mind if he is risk-averse. The longevity insurance allows people to smooth consumption over their natural lives and not worry about money running out at 85. When risk-averse people pool their risks together, it is possible that everyone gains regardless of who gets the payout in the end.

To sum up, don't worry about kicking the bucket at 84. Living till 85 and collecting the payout does not mean you have "won" either. If you are desperate for $250 at age 85, it means your money has already run dry - hardly an outcome you want.

36 Comments:

  • "It sometimes comes as a surprise to me how few people understand this principle. Even when I pose this question to a class of economics undergraduates, 80 per cent would get it wrong despite hours of lectures and classes on insurance."

    Being schooled in economics does not necessarily mean one is totally indoctrinated or buy into the rational or logic of economic thinking. And I suspect that it's only those with higher education economics training, and usually those who are more comfortable with quantitative methods, believes this is how the world should work if we want to achieve optimal efficiency and equity (global maxima?).

    Also, we should acknowledge the implications from experimental economics like traveller's dilemma have also shown that acting/thinking like the rational Economics person ala Homer Simpson actually leads to sub-optimal outcome for the players.

    There are more than a few papers written about the effects of economics education on undergrads and whether they think and act more like an economist after the course. I remember one paper that talks about Postgraduate Economics training in the context of the Chicago brand of economics vs other economics schools in the US.

    Yup, it's irrelevant to the point on Compulsory Annuities Scheme but thought I would point this little bit out.

    P.S: What do you reckon - it seems that many insurers (professionals or companies) in Singapore are actually ambivalent about this CAS, as compared to the reactions of economics trained people like you and Teh_Si in SingaporeAngle are lauding the scheme. Interesting diverge.

    By Anonymous ted, at 5:43 am  

  • Hi Ted,

    I am not sure about private insurers being ambivalent. Think about it, CAS has got nothing to do with private insurance at all.

    What CAS effectively does is to nationalise a part of CPF savings. Social Security, (US) National Insurance (UK) are examples. A part of yours and mine CPF savings becomes nationalised.

    I think I can understand why people might be upset. After all, who likes their assets to be nationalised. It feels like government forcefully seizing your assets doesn't it?

    Lucky kept saying that CPF is inadequate because of housing, healthcare etc. But that is not a fair assessment of what is the risks involved. It is silly to say that CPF system ok only if every one member has enough to live till 120.

    No one knows how long he/she is going to live. What is enough is a variable target - $x may be enough for some (if they live shorter), may not be enough for some (if they live longer). If every one lives till 85 and drop dead, the problem would be easily solved since every one knows how much to budget for.

    I hope that by explaining it rationally, people can realise that some nationalisation is a good thing - it allows us to share risks as a nation, rather than let the individual face the possibility of money running out after 85.

    By Blogger Bart JP, at 6:57 am  

  • There is no need for annuity scheme.

    let me explain......
    The min sum withdrawal age is delay from 62 to 65 and later to 67. It is said that for every one year of delay, the interest earned will enable withdrawal of another year ie to say 5 years delay will add another 5 years to the existing 20 years. If 5 years is too long a figure lets assume it to be 3 years instead. The withdrawal will last till 67 + 23 = 90 years of age.
    With a little reduction of the withdrawal amount from $790 to $650 or even $600, it should be able to last even longer.

    For those that are unable to meet the min sum (provided they buy a modest HDB flat) then the govnerment should help them.....isn't that the extra 2% GST is for..... ie to help the poor.

    By Anonymous Anonymous, at 8:19 am  

  • This comment has been removed by the author.

    By Blogger Bart JP, at 9:28 am  

  • Hi Anon,

    Need to be a little careful with the logic. This is not an accounting problem, it is a risk management issue.

    Even by your plan, risk is no eliminated. You can cut down withdrawal amount and push up withdrawal age, the risk is still there for the invidual. What happens after 90?

    Risk-pooling means using law of large numbers so that on balance, the system can fund everyone from 85 to the end of their natural lives. The individual would only need to budget from between retirement to age 85. Risk is removed from him.

    By Blogger Bart JP, at 9:31 am  

  • Bart,

    Thanks for explaining how annuity is a wonderful bet we should all take ...I'm sure the mathematics of it all makes sense.

    It would have made more sense if CPF is kept purely as a providence scheme for old age and not used for various purposes such as bailing out the economy during recessions, housing, children's education etc etc etc. We are here today because of all the tickering ...like I said I cannot deny that annuities can provide for the above 85, risk pooling or whatever you call it. It is why we have ended up here to have to do this that is amazing....

    By Blogger LuckySingaporean, at 9:56 am  

  • Lucky,

    I don't disagree with you in principle, maybe from the beginning, CPF should have been kept as simple as possible.

    But like the saying goes, you cannot put the shit back into the horse.

    Using CPF for housing, healthcare and education is pretty entrenched for decades already. So lets just work with the given realities. I am quite sure the annuity scheme can be done correctly to make it work.

    Above all, I do like the aspect about us pulling risks together as a nation. It is a form of helping each other.

    By Blogger Bart JP, at 10:01 am  

  • Lucky,

    Really cannot understand why you cannot seem to understand that given the rising costs of living, Singaporeans NEED access to their CPF money for housing and also cannot afford a higher contribution rate (to lock away more money). *sigh*

    In any case, doesn't matter whether you are right or you are wrong. We are where we are and we're got to figure out where to go from here.

    All your philosophizing about what should have been is a complete waste of time.

    By Blogger kwayteowman, at 1:21 pm  

  • annuity scheme is just a nice name. It is more like another form of retirement tax.

    Like I say in my earlier post on the delaying of the withdrawal age will last till 90 years of age.

    A further reduction of withdrawal amount to S$600 should last till 100. How many people can live past 100?

    if you still say it is not eliminating the risk of living beyond 100 then how about this....

    Since the interest earned per year for S$120,000 at 4%pa is S$4,800.
    S$4,800 divide by 12 will be S$400.
    By delaying a year of withdrawal, the person can withdraw a monthly amount of S$400 per month without touching the princial amount of S$120,000. This can last as long as the person lives.
    This is also better than the annity scheme of withdrawing an amount of S$250 - S$300 per month after 85.

    By Anonymous Anonymous, at 2:27 am  

  • When KTM cannot understand something, it must be that whoever who wrote it was stupid. Cannot be KTM is the stupid one, right? KTM is a smart brilliant genius.

    KTM is right: there is no point crying over spilt milk. But we be damned if we fail to identify the source of the problem and fail to rectify the same mistake. Let me quote a wise saying: "Fool me once, shame on — shame on you. Fool me — you can't get fooled again."

    The compulsory annuity is a meaningless distraction. How much is the pay out? $250-$300? In 30 years time? How many plates of char kway teow can I buy in 30 years time with $300? If I'm 85 today, I'm not even sure if $300 a month can keep me alive. What kind of insurance is that?

    Can a person's financial needs for decades be in predictably smooth amounts of a few hundreds a month?

    Does an unemployed Singaporean in his 40s really have to jump onto an MRT track just so that his family can get fed by his own money locked up in CPF?

    The government would be better off issuing suicide kits. Singapore can't afford to delay the train rides of our foreign talents.

    The CPF system should be abolished. After all, I thought some people believe that in a globalised world, citizenship does not matter any more. Then why penalise Singapore citizens with a compulsory CPF? Would HDB flats cost this much in the first place without being fueled by frivolous use of CPF funds?

    Why should employers be penalised with the CPF levy for hiring Singapore citizens? If CPF is so good, why dont we impose a flat rate on ALL workers in Singapore irregardless of citizenship/PRship?

    By Blogger Jimmy Mun, at 6:38 am  

  • Anon 2:27

    I am not sure if you are the same person as anon 8:19. I do understand what your logic is, but I cannot agree with you.

    If I have $100 savings, and I have $0 a month, it can last forever. Essentially, you are making the individual cut down his consumption to try to push his savings for as long as possible. The flip side is that if the individual budgets his savings to last till 100, and kicks the bucket at 70, he would have 30 years of unconsumed savings left! You have essentially made him save all these years for nothing.

    You cannot properly budget for consumption post retirement precisely because the date of death is unknown - it is a random variable.

    To ask every one to save as if they will live till 100 is inefficient. Risk-pooling is a far better mechanism. I hope you can see my point.

    By Blogger Bart JP, at 7:16 am  

  • Jimmy,

    I have spoken to some people about the annuity. Their concern is somewhat like yours - they are afraid that after contributing to the scheme, the government might move the goalpost again, say payout only at 90.

    I think the principle of the scheme is sound. But the government does have to assure people that (1) the premiums paid would be far (2) the commitment to payout at 85 is credible.

    Though $300 sounds little for you at the moment, but it can mean life and death for a person whose saving is running out at 85. The point of insurance is to guard against desperate outcomes. This is the point of insurance.

    By Blogger Bart JP, at 7:21 am  

  • Hi bart,

    How can insurance not be a zero sum game? It's like the casino, the house always wins. Of course you could get lucky and strike the million dollar jackpot. But the house still wins and the odds are stacked against the player. Otherwise who would be willing to be the insurer? Besides how about the time value of money? Insurance companies can still make a profit by investing their "float" even if the payout exceeds the premium collect.

    By Blogger I must be stupid, at 10:02 am  

  • Hi I-am-not-stupid,

    Insurance is such that it is possible that insurance companies make a profit, and the consumers who buy the insurance are still better off. It is not a zero sum game because consumers are risk-averse. By buying the insurance, risk is removed from them.

    Back to the care insurance example. The odds of me getting into a car accident is actually lower, hence car insurance companies do profit. However, I am still better off because I, being risk-averse, get the peace of mind.

    Unfortunately, you would probably need to go through an undergrad degree in econmics to be convinced of this point.

    By Blogger Bart JP, at 1:40 pm  

  • Hi bart,

    If you see it from the "car insurance" point of view, then i would understand your point of view. But i don't think i would need an economics degree to understand something like that.

    But aren't you defining that "having peace of mind" as 1 half of the win-win situation?

    The way i view this situation is that you are placing a $1 bet that gives u a 10% chance of winning $9. So if there's 100 placing such a bet, those 100 people if you take them as a whole will lose.

    Besides making everyone buy such an "insurance" would seem harldy fair to those with medical conditions that will guarantee that they will not live to get their payout. And if one exempts such "sure die young" cases from the scheme, the slippery slope situation will rear it's ugly head.

    How "sick" do you need to be to be exempted from that scheme?

    By Blogger I must be stupid, at 2:16 pm  

  • This comment has been removed by the author.

    By Blogger Bart JP, at 3:07 pm  

  • Hi bart jp,

    "Insurance is such that it is possible that insurance companies make a profit, and the consumers who buy the insurance are still better off."

    I have to disagree on this point. The purpose of insurance is to leave a person at a position where he is not worst off, never better off. That's why whenever someone's car get stolen in JB, he doesn't get back the amount he paid for the car but the amount he paid less depreciation or the equivalent price of the same-age car in the second hand market. However, most of the time, people will not get enough to be able to purchase the same car again.

    If insurance is such a perfect instrument, we won't be seeing people writing to newspaper to complain that they are unable to get fair compensation for their cars and in such incidents, peace of mind goes out of the window too.

    By Blogger peasantsgetowned, at 3:10 pm  

  • Hi Stupid,

    I am glad you see the point.

    You are also right in saying that some ill people probably will not see the money. For example, certain life-threatening genetic diseases can run in some families, which means that members have a systematically lower life expectancy compared to the rest of the population.

    Also, some researchers have suggested that the poor also lower life expectancy compared to the rich, because they lead more difficult lives and have less access to advance healthcare.

    In the end, the system will disadvantage these people. It is the acknowledged drawback of any nationalised retirement plans.

    To solve this problem, some modifications along the lines you suggested may be implemented. For example, if a citizen gets cancer at 40 and recovers, his contribution rate towards the scheme might be lowered. This is to recognise that his chances of living till 85 is lower due to the possibility of cancer relapse. His acturially fair rate of preimium for the old age annuity should be lower.

    But this might be administratively difficult.

    By Blogger Bart JP, at 3:12 pm  

  • Hi Peasant,

    The benchmark is not between stolen or non stolen cars like you mentioned. The benchmark is between with or without insurance!

    Consider this thought experiment. If your car is not stolen, it is worth $100k. If it is stolen, you get nothing.

    Suppose the insurance cost $1k. Now if your car is not stolen, you are left with $99k. If it is stolen, the insurance company compensates you $50k, not the full amount.

    If the person is risk averse enough, it is always possible to have a scenario where the person is better off with insurance than without. Without insurance, he risk a $100k vs $0 outcomes. People usually do not like that.

    By Blogger Bart JP, at 3:22 pm  

  • Of course, I am making the assumption that we do not get unscrupulous insurance companies or misselling of policies.

    By Blogger Bart JP, at 3:25 pm  

  • Hi bart,

    I see your point about risk hedging. But the reason why so many are unhappy with the annuities issue is that it is complusory. They do not have a choice. Many probably know that they have no hope of living beyond 85. Either old age and diseases takes them to their maker or the inability to afford medical care will do them in.

    What's gonna happen next? Compulsory health insurance? Where does this end? The main problem is the lack of choice involved. People general see that the cost involved in buying an annuities scheme is far higher that the potential benefits.

    Besides the implementation of the annuities scheme just masks the root of the problem, the low returns of CPF.

    By Blogger I must be stupid, at 10:54 pm  

  • Hi Bart,

    I am the same Anon at 8:19 and 2:27. Good that you see my logic.

    However, you still do not see my point of view. Retirement saving and plannig is always about consuming within our means instead of excessive spending.

    It does not hurt if I am to leave ealier as I will be leaving a sum of money to my children.

    Your agurement that consuming less is inefficient does not make any sense. If I am to use your same logic, then why is our Govt keeping so much money in the reserve.

    Anyway, there is another suggestion from Mr Leong Sze Hian (President of the Society of Financial Service Professionals)
    He suggests that there is no need for a compulsory annuity scheme, and that the same payouts can be achieved via existing CPF accounts
    "Instead of spending the S$750 million a year to pay the additional 1 per cent interest on the first S$20K of CPF Ordinary account and S$40k of the special, medisave and retirement accounts, growing these sum at say, 5 percent interest will accumulate to S$67.6 billion in 2042. This is the first year that the compulsory annuity will start at age 85, for those who are below 50 yrs old now.
    At 5 per cent interest, the S$67.7 billion could provide S$300 a month from age 85 to 100 for 1.79 million Singaporeans.

    Bottom line: there are creative ways to solve this issue instead of compulsory annuity scheme.

    By Anonymous Anonymous, at 2:32 am  

  • This comment has been removed by the author.

    By Blogger Bart JP, at 2:41 am  

  • Hi Anon,

    I agree with you that you can leave unconsumed savings for children. But if there are indeed children, old age destitution is probably less of a concern. There are many singles, so there is a genuine risk they face.

    Between increasing returns and risk-pooling, I actually think risk-pooling is the more creative and more efficient solution. But we can agree to disagree on this.

    By Blogger Bart JP, at 2:43 am  

  • Hi Bart JP

    If you are comparing having a stolen car that is worht 99k after insurance and you get back 50k, how is that suppose to be better off?

    Risk has not been removed as you have lost 44K even though you bought insurance. Even if you did not crash the car, the risk has been paid for with $1000.

    By Blogger peasantsgetowned, at 8:31 am  

  • Hi Peasant,

    Don't compare between stolen and non-stolen.

    Compare between with or without insurance. Without insurance, he faces more extreme outcomes $100k or nothing. With insurance, he faces less extreme outcomes, hence some risk is removed.

    Usually, because of moral hazard problem, the insurance companies will not remove all risks for the consumer. If he still gets $100k compensation if he loses the car, he has no incentive to take care of it.

    By Blogger Bart JP, at 8:59 am  

  • Hi bart,

    Perhaps it would be more accurate to describe insurace as hedging the risks.

    In terms of probability, the insured still loses.

    Of course you could say it's better to have a high chance to lose abit than to have a low chance to lose it all.

    Then i would suppose that you are a fan of 4D or toto or any of the games found in a casino. Better to have a high chance to lose a little than to forgo the chance of winning big time.

    By Blogger I must be stupid, at 9:46 am  

  • Hi Bart,

    The reason for buying insurance is to leave you in a position of no gain or loss in the event of an accident happening.
    The point is that overall, the insuree still loses, just that he loses less. Your point, if i am not wrong, is that losing less is itself winning as you have insured against part of the risk.

    By Blogger peasantsgetowned, at 9:55 am  

  • Bart, KwayTeowMan,

    You guys are so right....I'm harping on the past...shit can't be put back in the horse. Just that I was among the vocal...just can't get over what could have and should have been done right.

    Annuities, tax, insurance - take money from the majority give to those who need. ...I can't understand why there is a debate even before the scheme details are announced. The govt can dress it up as tax and do the same thing. I just hope this is not one of the kiasu govt scheme where the squeeze everyone and give out very little to those who need it...then end up with a surplus ...just like they did in eldershield and had to return all that money. The worst thing they can do is put this under some insurance company who are known to make fat margins off such schemes. I wonder sometimes if there is a conflict of interest because of the close ties of PAP with some of these businesses like NTUC income.

    Some people are viewing this negatively - yet another scheme to prevent people from getting their CPF. Well if the PAP wants to squeeze you, they can do so many other ways. I think the ERP probably collects more money than this annuity thing.

    Bart, no need to try to explain annuities, risk pooling concepts to people. They either get it or they don't. It is as simple as fire insurance, car insurance....the devil is in the details - the price of this insurance. I've no liking for insurance companies. When I was a poor feller, I bought it because I had no choice - I had to sleep soundly at night and was forced to take a few raw deals. I would have preferred to be self insured.

    Any annuity scheme introduces a middle man who shave off some for their trouble...it took almost 20 years for PAP to realise the management fees charge by CPF approved unit trusts were absurdly high - some of the fund managers even charge advertising cost to the CPF investors resulting in pathetic returns for investors. The govt stepped in 20 years later to rein in the management fees.

    Sorry guys, I always look at the past to see the future. Lessons not learnt will always be repeated.

    By Blogger LuckySingaporean, at 11:03 pm  

  • Lucky,

    Absolutely. Need to see the premium first.

    I was explaining the scheme in principle, and trying to clear some misunderstanding.

    By Blogger Bart JP, at 12:50 am  

  • Bart,

    Okay. But I haven't met anyone who can't understand the idea. They just don't like it and I believe they dislike being forced into it against the backdrop of being told "sorry lah work longer, your CPF is not enough for you to retire"...."now please buy these annuities..you have no choice, it is good for you".

    Bart, save your breathe. The sentiment is just no good lah...

    By Blogger LuckySingaporean, at 2:03 am  

  • Thanks Lucky. I am aware the sentiments are not good. By highlighting the economic case rationally, maybe I can convince some to accept it in their heads (if not their hearts) that CAS is a good plan.

    By Blogger Bart JP, at 5:47 am  

  • Hi Bart

    Under the heading All Can Be Better Off, you sum up your post with the fact that If you are desperate for $250 at age 85, it means your money has already run dry - hardly an outcome you want .
    Meaning even you accept $250 will be little more than a useless gesture.

    I assume the "All" in your header refers to the Gahmen who transfer the responsbility of looking after the weakest members of the society to the citizens?

    Of course it makes perfect economic sense.

    PS:
    Please understand only Liverpool fans bet against their team for a couple of dollars. For any other football teams, it automatically disqualify them as "fans\supporter". Maybe only 20%of your class supports Liverpool. Most fans in democratic societies has a 3rd option - dun bet.

    NoName

    By Anonymous Anonymous, at 3:15 am  

  • Noname

    $250 is not a usless guesture. When one has zero savings left, $250-$300 a month can be a lot - the utility from the first dollar is the highest.

    Anyway, I disagree with your assertion that Govt is transferring responsibility to society. Govt is part of society, it is not an out of the country participant. Its effects are mainly through redistribution - ie from some segments of the economy to other segments.

    For the government to spend on the growing number of old people, it has to draw revenue somewhere - ie from the rest of citizens eventually. Whether the funding comes from general taxation or from CPF is, in the larger scheme of things, not any different.

    Of course at this point, some would jump and bring out reserves, Temasek, GIC etc. I am not going to go into the whole debate how much reserves is enough or any governance issues concerning reserves.

    Suffice to say that population ageing is a long term problem that needs a long term solution. If govt can work out the right formula for CAS to acturially fund itself, without premiums being excessively high, it must count as a plus to build into the system.

    By Blogger Bart JP, at 3:44 am  

  • Nevermind the value of $250 after 30 years of inflation. Say you meet a desperate 85 year old on the street, would you help?

    The question is how many desperate 85+ year olds (w/o support) will there be in say 30 years.

    Now, if we follow the doomsday scenario favored by your leaders ... say more than 50% of the oldies are desperate. Do you know what that means?

    It means either
    1. Singapore is so morally bankrupt that she no longer cares about the weakest members. The aged are abandoned by family and society.

    2. Singapore is so financially bankrupt that she could no longer care.

    Either way the little red dot will no longer be viable. annuitiy or no annuity.

    Given the ever widening wealth disparity, rising cost of living and the disconnect between the gahmen and the poor ... how would it be possible to work out the right formula for CAS to acturially fund itself, without premiums being excessively high and achieve a meaningful payout that satisfies the needs of the "desperate"?

    Remember, Singapore already has one of the highest saving rates in the world. As much as you wou like to frame your argument within a favorable context, the reality is that there is no escaping the fact that the gahmen has to 1.look at the cost structure (stretch retirement dollars ,not more asset inflation pls) and 2. increase the returns on our savings. Fundamental changes are needed.

    Otherwise compulsory annuities would be just like using the ERP to solve traffic jams on the CTE. Not very useful.

    NoName

    By Anonymous Anonymous, at 6:37 am  

  • Well, guys, what a load of bullcrap we have been discussing. Apparently the GIC holds an estimated US$330 billion bucks worth of assets and cash. And here we are pontificating on the merits and demerits of the CAS for OLD people above 85. Well done, well done!

    http://www.todayonline.com/articles/209819.asp

    By Anonymous ted, at 5:47 am  

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